A parked car packed with explosives was detonated by remote control as the police bus drove by on Tuesday, CNN Turk said.
The blast occurred during the morning rush hour in the densely populated district. Gunshots were heard in the area after the blast, according to state-run Anadolu Agency.
The area is a commercial hub as well as the location of Istanbul University and is close to key tourist sites like the Grand Bazaar.
There was no immediate claim of responsibility but Kurdish militants, Daesh extremists and radical leftists have all staged attacks in Turkey recently.
Turkey has suffered a spate of bombings this year, including two attacks in tourist areas of Istanbul blamed on Daesh and two car bombings in the capital, Ankara, which were claimed by a Kurdish militant group.
The attacks have come as Turkey is battling PKK militants, who have killed hundreds of members of the security forces in the southeast.
Bombings in Turkey's heartland have had a dire effect on the tourism industry and further violence in Istanbul comes at the worst possible time heading into the key summer season.
According to the Tourism Ministry, some 1.75 million foreigners came to Turkey in April, down more than 28 percent on April 2015.
The fall was the steepest monthly decrease for 17 years and raised fresh concerns about the health of the industry heading into the crucial summer season.
The US embassy in Turkey in April warned of "credible threats" to tourist areas in Istanbul and the resort city of Antalya, in particular to public squares and docks.
Turkey, a member of NATO and the US-led coalition, has stepped up its operations in northern Syria.
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